Microcanonical Rate Constants for Unimolecular Reactions in the Low-Pressure Limit

Low-pressure-limit microcanonical rate constants, κ₀(E,J), describe the rate of activating bath gas collisions in a unimolecular reaction and are calculated here using classical trajectories and quantized thresholds for reaction. The resulting semiclassical rate constants are two-dimensional (in total energy E and total angular momentum J) and are intermediate in complexity between the four-dimensional state-to-state collisional energy and angular momentum transfer rate constant, R(E',J';E,J), and the highly averaged thermal rate constant, k₀. Results are presented for CH₄ (+M), C₂H (+M), x = 3-6, and H₂O (+M), where κ₀(E,J) is shown generally to be a sensitive function of the bath gas, temperature, and initial state of the unimolecular reactant. Strong variations in κ₀ with respect to E and J lead to complex trends in relative microcanonical bath gas efficiencies. This underlying complexity may complicate the search for simple explanations for observed trends in relative thermal bath gas efficiencies. A different measure of the microcanonical collision efficiency that describes the energy range of activating collisions is introduced that supports the empirical decomposition of collisional activation into separable translational-to-vibrational and rotational-to-vibrational activation mechanisms. The two mechanisms depend differently on mass, temperature, and the J-dependence of the threshold energy for reaction, with rotational-to-vibrational activation favored for heavier baths and for reactions with rigid transition states. Finally, κ₀ is used to test the accuracy of several two-dimensional models for R that were proposed for use in master equation studies.